Search Results (17)

The purpose of this paper is to address conflicting results regarding a simple criterion that has been proposed as decisive in determining whether accounting for spiralling electron trajectories increases or decreases the widths of hydrogen lines in a parameter range relevant to the spectral lines of white dwarfs. We analyse the claims in detail and also provide explicit calculations. It is shown that the recent attempts to justify a simple theory are erroneous and miss important physics. Full article

It has been recently suggested that white dwarf diagnostics could be in error and should be revised because of the effect of the magnetic field on spiralling trajectories of the plasma particles (mainly electrons), predicting a dramatic width increase for high densities of Balmer-$\beta$ and especially for the $\delta$ and $ϵ$ lines. These suggestions overlook important physics and are shown here to be incorrect. Specifically, exact calculations are carried out that can assess the importance of various physical effects neglected in the erroneous analysis mentioned. The net result of accounting for spiralling electron trajectories is typically a small to modest reduction in the line widths, at least for the parameters considered. Full article

The present review is dedicated to the problem of an array of transitions between highly-excited atomic levels. Hydrogen atoms and hydrogen-like ions in plasmas are considered here. The presented methods focus on calculation of spectral line shapes. Fast and simple methods of universal ionic profile calculation for the $H_{n\alpha }$ ($\mathsf{\Delta }n=1$) and $H_{n\beta }$ ($\mathsf{\Delta }n=2$) spectral lines are demonstrated. The universal dipole matrix elements formulas for the $H_{n\alpha }$ and $H_{n\beta }$ transitions are presented. A fast method for spectral line shape calculations in the presence of an external magnetic field using the formulas for universal dipole matrix elements is proposed. This approach accounts for the Doppler and Stark–Zeeman broadening mechanisms. Ion dynamics effects are treated via the frequency fluctuation model. The accuracy of the presented model is discussed. A comparison of this approach with experimental data and the results of molecular dynamics simulation is demonstrated. The kinetics equation for the populations of highly-excited ionic states is solved in the parabolic representation. The population source associated with dielectronic recombination is considered. Full article

Stark broadening of Lyman-$\alpha$ of a hydrogen-like atom in the presence of a strong magnetic field is analyzed. The shape of the central ($\pi$) component of the Lorentz–Zeeman triplet is expressed analytically, taking into account the plasma coupling and microfield dynamic effects. It is shown that in a sufficiently strong magnetic field, the broadening of this component, contrary to the broadening of the lateral ($\sigma$) ones, is independent of the magnetic field and, therefore, can be used for the plasma density diagnostics. Comparison with computer simulations at conditions typical for tokamak divertors and white dwarf atmospheres shows a very good agreement. Full article

In this non-exhaustive review, we discuss the importance of invariant vectors in atomic physics, such as the Laplace–Runge–Lenz vector, the Redmond vector in the presence of an electric field, the Landau–Avron–Sivardièrevector when the system is subject to a magnetic field, and the supergeneralized Runge–Lenz vector for the two-center problem. The application to the Stark and Zeeman effects are outlined. The existence of constants of motion in the charge-dyon system is also briefly mentioned. Full article

We propose a scheme to generate and control high-dimensional rogue waves in a coherent three-level $\mathsf{\Lambda }$-type atomic system via electromagnetically induced transparency (EIT). Under EIT conditions, the probe field envelopes obey the non-integrable nonlinear Schrödinger equations (NLSE) with or without the external potential, which result from the stark (Zeeman) effect contributed by an electric (magnetic) field. By adjusting the amplitude and width of the initial pulse, we can generate the high-dimensional rogue waves and obtain the phase-transition curves of high-dimensional rogue waves. In the system, the far-detuned electric field, the random weak magnetic field, and the Gauss weak magnetic field are not conducive to the excitation of high-dimensional rogue waves. The results not only provide a theoretical basis for the experimental realization or prevention of the high-dimensional rogue waves, but also prove the possibility of generating and controlling the rogue waves in other high-dimensional non-integrable systems. Full article

Free electron systems are ubiquitous in nature and have demonstrated intriguing effects in their collective interactions with weak electric and magnetic fields, especially in aqueous environments. Starting from the Dirac Hamiltonian, a fully relativistic expression is derived for the electron energy shift in the presence of a spatiotemporally constant, weak electromagnetic field. The expectation value of this energy shift is then computed explicitly using the Fourier transforms of the fermionic fields. To first order in the electromagnetic fields, the average relativistic energy shift is found to be completely independent of the electron spin-polarization coefficients. This effect is also considerably larger than that predicted in quantum mechanics by the analogous Zeeman shift. Finally, in the non-relativistic limit, it is shown how to discriminate between achiral and completely polarized states, which leads to a concluding discussion of possible mesoscopic and macroscopic manifestations of electron spin states across many orders of magnitude in the physical world, with stark implications for biological and other complex systems. Full article

In this work, we studied the Lyman-alpha line in the presence of a magnetic field, such as the ones found at the edge of tokamaks. The emphasis is on the contribution of the motional Stark effect on line broadening, which may have comparable effects to the internal plasma microfields for the spectral line in question. The effect of the magnetic field, temperature, and the Maxwell distribution of the ion velocities and density on Lyman-alpha are studied. Full article

A new method of line shape calculations of hydrogen-like atoms in magnetized plasmas is presented. This algorithm makes it possible to solve two fundamental problems in the broadening theory: the analytical description of the radiation transition array between excited atomic states and an account of a thermal ion motion effect on the line shapes formation. The solution to the first problem is based on the semiclassical approach to dipole matrix elements calculations and the usage of the specific symmetry properties of the Coulomb field. The second one is considered in terms of the kinetic treatment of the frequency fluctuation model (FFM). As the result, one has a universal description of line shapes under the action of the dynamic of ion’s microfield. The final line shape is obtained by the convolution of the ionic line shape with the Voigt electron Doppler profile. The method is applicable formally for large values of principal quantum numbers. However, the efficiency of the results is demonstrated even for well known first members of the hydrogen Balmer series $D_{\alpha }$ and $D_{\beta }$ lines. The comparison of obtained results with accurate quantum calculations is presented. The new method may be of interest for investigations of spectral line shapes of hydrogen-like ions presented in different kinds of hot ionized environments with the presence of a magnetic field, including So L and divertor tokamak plasmas. Full article

We report on hydrogen line shape calculations in the presence of an external magnetic field, at conditions such that the quadratic Zeeman effect is important. The latter is described through a term proportional to B² in the Hamiltonian, accounting for atomic diamagnetism. It provides a shift and an asymmetry on Lorentz triplets, and it leads to the occurrence of forbidden components. Motivated by investigations performed at the fifth edition of the Spectral Line Shape in Plasmas (SLSP5) code comparison workshop, we perform new calculations of hydrogen Lyman line profiles. Field values representative of magnetized white dwarf atmosphere conditions are taken. The calculations are done using a computer simulation technique, designed for Stark broadening modeling. A discussion of the results is done in the framework of plasma diagnostics. Full article

This article proposes a new method for sensing THz waves that can allow electric field measurements traceable to the International System of Units and to the fundamental physical constants by using the comparison between precision measurements with cold trapped HD⁺ ions and accurate predictions of molecular ion theory. The approach exploits the lightshifts induced on the two-photon rovibrational transition at 55.9 THz by a THz wave around 1.3 THz, which is off-resonantly coupled to the HD⁺ fundamental rotational transition. First, the direction and the magnitude of the static magnetic field applied to the ion trap is calibrated using Zeeman spectroscopy of HD⁺. Then, a set of lightshifts are converted into the amplitudes and the phases of the THz electric field components in an orthogonal laboratory frame by exploiting the sensitivity of the lightshifts to the intensity, the polarization and the detuning of the THz wave to the HD⁺ energy levels. The THz electric field measurement uncertainties are estimated for quantum projection noise-limited molecular ion frequency measurements with the current accuracy of molecular ion theory. The method has the potential to improve the sensitivity and accuracy of electric field metrology and may be extended to THz magnetic fields and to optical fields. Full article

Contemporary spectroscopic studies of astrophysical and laboratory plasmas frequently deal with extremely large values of principle quantum numbers of atomic systems. These atomic states are very sensitive to electric and magnetic fields of the surrounding medium. While interpreting the spectra of such excited atomic systems, one faces the problem of a huge array of radiative transitions between highly excited atomic levels. Moreover, external electric and magnetic fields significantly complicate the problem because of the absence of standard selection rules typical for the spherical quantization. The analytical expression in the parabolic representation for dipole matrix elements obtained by Gordon contains hyper-geometric series and it has a very complex structure. The matrix elements that involve the presence of electric and magnetic fields are calculated while using a representation closely related to the parabolic quantization on two different axes. This matrix element depends in a complex way on the transition probabilities in the parabolic coordinate system (Gordon’s formulas) and the Wigner d-functions. This circumstance leads to even greater computational difficulties. A method of simplification of these complicated expressions for transition probabilities is demonstrated. The semiclassical approximation for coordinate matrix elements (Gulayev) and recurrence properties of the Wigner d-functions are used. The $H_{n\beta }$ line is under consideration. Specific calculations for the transition 10–8 in the case of parallel and perpendicular fields are presented. Full article

There is presented an overview of the latest advances in the analytical theory of Stark broadening of hydrogenic spectral lines in various types of laboratory and astrophysical plasmas. They include: (1) advanced analytical treatment of the Stark broadening of hydrogenic spectral lines by plasma electrons; (2) center-of-mass effects for hydrogen atoms in a nonuniform electric field: applications to magnetic fusion, radiofrequency discharges, and flare stars; (3) penetrating-ions-caused shift of hydrogenic spectral lines in plasmas; (4) improvement of the method for measuring the electron density based on the asymmetry of hydrogenic spectral lines in dense plasmas; (5) Lorentz–Doppler broadening of hydrogen/deuterium spectral lines: analytical solution for any angle of observation and any magnetic field strength, and its applications to magnetic fusion and solar physics; (6) Revision of the Inglis-Teller diagnostic method; (7) Stark broadening of hydrogen/deuterium spectral lines by a relativistic electron beam: analytical results and applications to magnetic fusion; (8) Influence of magnetic-field-caused modifications of the trajectories of plasma electrons on shifts and relative intensities of Zeeman components of hydrogen/deuterium spectral lines: applications to magnetic fusion and white dwarfs; (9) Influence of magnetic-field-caused modifications of trajectories of plasma electrons on the width of hydrogen/deuterium spectral lines: applications to white dwarfs; (10) Stark broadening of hydrogen lines in plasmas of electron densities up to or more than N_e~10²⁰ cm⁻³; and, (11) The shape of spectral lines of two-electron Rydberg atoms/ions: a peculiar Stark broadening. Full article

In plasmas subject to a strong magnetic field, the dynamical properties of the microfield are affected by the cyclotron motion, which can alter Stark-broadened lines. We illustrate this effect through calculations of the hydrogen Lyman $\alpha$ line in an ideal one-component plasma. A focus is put on the central Zeeman component. It is shown that the atomic dipole autocorrelation function decreases more slowly if the cyclotron motion is retained. In the frequency domain, this denotes a reduction of the line broadening. A discussion based on numerical simulations and analytical estimates is done. Full article

We present the ZEST code, dedicated to the calculation of line shapes broadened by Zeeman and Stark effects. As concerns the Stark effect, the model is based on the Standard Lineshape Theory in which ions are treated in the quasi-static approximation, whereas the effects of electrons are represented by weak collisions in the framework of a binary collision relaxation theory. A static magnetic field may be taken into account in the radiator Hamiltonian in the dipole approximation, which leads to additional Zeeman splitting patterns. Ion dynamics effects are implemented using the fast Frequency-Fluctuation Model. For fast calculations, the static ion microfield distribution in the plasma is evaluated using analytic fits of Monte-Carlo simulations, which depend only on the ion-ion coupling parameter and the electron-ion screening factor. Full article